Mathematical Sciences: Presidential Young Investigator Award

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The investigator will study computational fluid dynamics problems centering on shock wave propagation and transonic flow, and also the partial differential equations that describe semiconductor devices. These equations are similar to the equations of fluid dynamics and many of the numerical techniques useful in one case carry over to the other. Numerical calculations and the development of algorithms are a major part of these studies. Computational fluid dynamics undertakes to determine numerically the solution of the differential equations that describe the motion of a fluid, particularly in cases where the solution cannot be written down explicitly. Such difficult cases are the rule for the fluid dynamics problems that arise in practice. Applications in which shocks occur are common. Transonic flow problems arise in aerospace design. In the area of semiconductors, the project work has applications in resolving several different semiconductor models and in the fabrication of semiconductors.